Beyond the ensemble paradigm in low dimensional quantum gravity: Schwarzian density, quantum chaos and wormhole contributions

TL;DR

This paper explores the connection between quantum chaos and low-dimensional quantum gravity, showing how spectral properties and wormhole geometries relate to dualities between single systems and ensembles.

Contribution

It demonstrates a duality between quantum chaos signatures in geodesic spectra and gravitational models like JT gravity, extending understanding beyond ensemble averages.

Findings

Spectrum exhibits Schwarzian mean level density

Universal signatures of quantum chaos are observed

Wormhole geometry emerges from periodic orbit discreteness

Abstract

Based on periodic orbit theory we address the individual-system versus ensemble interpretation of quantum gravity from a quantum chaos perspective. To this end we show that the spectrum of geodesic motion on high-dimensional hyperbolic manifolds, described by the Selberg trace formula, displays a Schwarzian ($\sinh 2\pi\sqrt{E}$) mean level density. Due to its chaotic classical limit, this quantum system also shows all universal signatures of quantum chaos. These two properties imply a possible duality to Jackiw-Teitelboim-type quantum gravity at the level of a single system instead of an ensemble of systems like matrix theories and SYK models. Beyond the universal regime we show how the full wormhole geometry on the gravity side emerges from the discreteness of the set of periodic orbits. Thereby, we take initial steps towards a duality between gravitational and mesoscopic chaotic quantum systems through the topological, respectively, periodic orbit expansions of their correlators.